Problem:
When standard -sided dice are rolled, the probability of obtaining a sum of is greater than zero and is the same as the probability of obtaining a sum of . The smallest possible value of is
Answer Choices:
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Solution:
When dice are rolled, the sum can be any integer from to . The sum can be obtained in the same number of ways as the sum , and this number of ways increases as increases from to . Minimize by choosing and as small as possible with . Since the least multiple of that is greater than or equal to is , is smallest when and . Consequently, .
On a standard die, and and , and and are on opposite sides. To obtain a sum of with the most sixes on the top faces of the dice requires that sixes and two face up. Then ones and five will face down, and .